Diving into Bitcoin Halving Calculations

So I saw this interesting reply from hugeblack yesterday. He posted a pic of the Bitcoin halving formula. I got super curious and wanted to crunch some numbers on how Bitcoin halves every four years. Turns out, this formula might help us figure out the total supply too.

It’s a bit different from what hugeblack posted, but honestly, it gives the same result. The 108 variable cancels itself out. The cool part is you can easily find total supply without needing to plug in values for each halving period.

Hold up, but I think you got the math wrong. The second period actually produced 5,250,000 BTC, not that 5249999.998 number. The total ends up being around 21 million after all halvings.

21 million is a round number, no decimals, remember? Just saying that number is an estimate.

I thought you were referring to your own paper where x=2 is the second period. I don’t see the point in summing from x=2 to x=32.

Yeah I know 21 million doesn’t have decimals. I was talking about block rewards though. After the 10th halving, the reward is 0.048828125 BTC, which rounds to 0.04882812 BTC.

Haha, I went a bit wild with this too. Said it was a bit much, but honestly, I had fun.

That wiki page claims global gold production is fixed more than it drops exponentially. Seems legit.

You’re missing a key point: altcoins. Each serious altcoin kinda messes with that 21 million limit. If Bitcoin holds 50% market dominance, that’s like having 42 million across the board, but a lot of it’s off-chain.

The infinite sum is right, but Bitcoin Core caps it at 64 halvings. After 33 halvings, the subsidy goes to zero, so max supply ends up slightly less than 21 million.

Phew, glad I got that infinite sum right. My calculator must’ve done the truncation automatically when I calculated all 33 halvings. Decimals popped up when I broke it down for each halving.

Your values might be off cause your calculator isn’t precise enough for those numbers.

It's likely just a rounding error due to hardware limitations. Small inaccuracies happen.

I checked OP's series for 210,000*50/(2^x) from x=2 to x=32 and got 5249999.998. I used Python and got 5249999.997555278. At first, I thought x=2 meant the second halving.